# Focus of Parabolic Reflector Calculator

## Formula for the Focal Distance of a Parabolic Reflector Given its Depth and Diameter

The equation of a parabola with vertical axis and vertex at the origin is given by

\( y = \dfrac{1}{4f} x^2 \)

where \( f \) is the focal distance which is the distance between the vertex \( V \) and the focus \( F \).

Let \( D \) be the diameter and \( d \) the depth of the parabolic reflector. Using the diameter \( D \) and the depth \( d \), the point with coordinates (D/2 , d) is on the graph of the parabolic reflector and therefore we can write the equation

\( d = \dfrac{1}{4f} D^2 \)

Solve for \( f \) to obtain

\( f = \dfrac{D^2}{16 d} \)

## How to Use the Focal Distance Calculator

Enter the depth d and the diamter D as positive real number and click on "Calcualte". The answer is the focal distance f.

Note that \( D \) and \( d \) must be of the same unit. Both meters, or centimeters, or feet...

The default values are in centimeters.

## More References and Links to Parabola

Equation of a parabola.

Tutorial on how to Find The Focus of Parabolic Dish Antennas.

Tutorial on How Parabolic Dish Antennas work?

Three Points Parabola Calculator.

Use of parabolic shapes as Parabolic Reflectors and Antannas.